If driving doesn’t recharge a battery is there any point putting it on a charger?
The alternator on your car will typically output a comparatively large current when it's recharging a battery and a battery in good condition can take it, and recharge quickly. This means a car used for frequent short journeys such as postal worker, door to door community nurse, or delivery driver makes don't leave them with a flat battery.
A battery that is in worse condition, older or has been run down quite flat one or more times (and unless it's designed for deep discharge such as a leisure battery that powers items on a boat, golf cart, mobility buggy etc we're not talking about much here - a standard lead acid cell depleted to less than 75% will start to suffer/become ruined. Leisure batteries might have a threshold of more like 30%) will be more easily damaged by a high rate of charge; it's possible to overheat and warp the plates inside the cells, causing internal shorts or increase the amount of she'd sediment that collects in the bottom of the cells. Batteries that are discharged below the design threshold tend to suffer from a process called sulfation, where the sulfur from the acid binds (generally) irreversibly to the lead in the plate; this means the charge holding capacity of the battery is diminished and even though a volt meter might read a good voltage for it, it won't supply as many amps or for as long as a new battery. Particularly in winter, when electrical demands are high and ambient temperatures mean that the internal resistance of (and hence voltage that can develop across) a battery is lower, mean that the battery will no longer supply sufficient power for the highest drain scenario; starting the car
Chargers typically charge at a much lower rate than an alternator would, which may be favorable to recovery of a discharged battery. There are a good number of snake oil products that claim to be able to revive a sulfated discharged battery, but mostly they're junk. There isn't a way to recover a heavily sulfated battery to perfect health but you might achieve an improvement in it by charging it for a long time on a low output old style (dumb) charger and monitoring the current flow into the batteries. They tend to exhibit a pattern of accepting current then dropping to very low acceptance, rising again and then tapering off. The first peak is the charging of whatever capacity it has at the moment, the drop is that it can't accept any more charge in its present state(and that's when a smart charger will switch mode to maintain it, and why dumb chargers do better for this), the second rise being where some of the sulfation reverses and charge acceptance improves, and the second fall in current being when there is no more recovery possible. Depending on how long the battery was left inna discharged state, it might have a useful capacity recovery at the end of this, or it might not
You've noted that your battery gets better and better, but you didn't really explain what your metric for this is. It might also be dependent on some environmental factor such as warming weather, but to answer you question of "is there any point bench charging a battery if the car doesn't charge it", I say perhaps yes because bench charging at a low rate stands a better chance of recovering a discharged battery without damaging it internally and because a bench charge can be carried out over the necessarily lengthy amount of time compared to driving a car for an hour, stopping it, having the parasitic drain from alarms etc, the stress of starting the car, charging it for another hour as it runs, lather rinse repeat
You didn't say what the history of this battery was but if I'd deep discharged a car battery and realized I wouldn't consider "jump start it and take it for a long drive to charge it" - it'd be bench charged at less than 1 amp for as long as required. If you can catch a discharged battery soon and recharge it slowly it will recover, though probably not to the level it was before
Also worth noting that instantaneous voltage is a poor indicator of a battery's overall condition; a series of 8 torch batteries will read 12v, but wouldn't start a car. The voltage under load is a better indicator, but measuring the current delivery profile is best; a battery is designed to deliver a certain amount of current for a certain time and it's written on a sticker on the battery. If you're discovering that an 80
amp-hour capacity battery can deliver 10 amps for 10 minutes (approximately ten minutes of two 60w bulb headlight use) then it's toast; even if it's registering a voltage of 13v at the start, it's got a capacity more like a 4Ah motorcycle battery
Battery chemistry is a huge topic, far more can be said than is in scope for an SE answer; entire websites exist to talk about it, so this is just a surface skimming to answer the question as presented